Protesters head to Hotel Bel-Air over Islamic law

The boycott of the Beverly Hills Hotel and the Hotel Bel-Air over their owner's ties to severe Sharia punishments in Brunei will take to the streets in California on Thursday, even as a chorus against the boycott is also gaining followers.

Stonewall, a gay, lesbian and bisexual rights charity in the U.K., said it condemns the Sharia rules in Brunei but opposes the boycott against the London-based luxury chain. Actor Russell Crowe on May 19 also tweeted his opposition to the boycott. "I don't agree with the boycotting of Dorchester Collection hotels. It only hurts the hard working staff who I consider friends."

At issue is the 10 luxury hotels in the Dorchester Collection, which is owned by the Brunei Investment Agency, a branch of the government. Brunei, an oil-rich country in Southeast Asia, recently began phasing in very strict penalties for violating Islamic law (Sharia), including stoning and death sentences for crimes including adultery and sodomy.

The Unite Here Local 11 hospitality union plans to press for the boycott Thursday at the Hotel Bel-Air by handing out leaflets to incoming lunch guests. The union formerly represented workers at the hotels.

"Business, particularly meetings and events, continues to be impacted," Leslie Lefkowitz, a spokeswoman for Dorchester, told CNBC by email Thursday. "There is very little impact to the other hotels in Europe."

There are hundreds of other properties frequented by Hollywood's elite that are owned by companies with strong ties to Islamic law, said Eric Schiffer, CEO of ReputationManagementConsultants.com, which advises companies on topics like this. Schiffer is not working with Dorchester on this matter.

Hollywood stars boycott famed Beverly Hills hotel

CNBC's Morgan Brennan interviews the Dorchester Group CEO Christopher Cowdray about the hotel's owner, the Sultan of Brunei, who recently instituted an extreme form of Islamic law (Sharia) in his country.

"These laws are barbaric and unfortunate," Schiffer told CNBC. "I think this is something of a knee-jerk reaction rather than a strategic battle plan to effect the laws. ... There are better targets that are frequented by Hollywood."

On May 16, Stonewall's acting chief executive, Ruth Hunt, wrote in London's Telegraphthat dialogue with the hotel is more effective than a boycott. "We're renowned for our pragmatism and our belief that talking is usually more effective than protests—however satisfying protests may be, in the short term they're often most rewarding to the individuals taking part," Hunt wrote in an op-ed.

"By turning the issue into a battle between gay people and the Sultan—which it isn't, it affects everyone in Brunei, not just gay people—we limit the opportunity for dialogue and put the lesbian, gay, bisexual and trans people of Brunei at far greater risk," she wrote in the piece.